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Charm hadrons in nuclear medium arXiv:1308:0098 [hep-ph] S. Yasui (KEK) K. Sudoh (Nishogakusha Univ.) “Hadron in nucleus” workshop@YITP, 31 Nov. – 2 Dec. 2013 Contents 1. Introduction to charm (bottom) nuclei 2. Mass formula with 1/mQ expansion 3. Anti-D (B) meson in nuclear medium - Heavy meson effective theory with 1/M corretions 4. Summary & perspectives 1. Introduction to charm (bottom) nuclei D(*) (B(*)) meson in nuclear matter 1. D (B) meson and nucleon interaction 2. Modifications of D (B) meson chiral condensate, gluon condensate, ... 3. Modifications of nuclear structure glue-like role? → L. Tolos A. Yokota Y. Yamaguchi K. Suzuki Cf. Kondo effect K.Sudoh, S.Y., PRC88, 015201 (2013) 1. Introduction to charm (bottom) nuclei D(*) (B(*)) meson in nuclear matter → L. Tolos A. Yokota Y. Yamaguchi K. Suzuki SY and Sudoh, PRC87, 105202 (2013) Binding energy of D(*) (B(*)) meson in nuclear matter (MeV) Quark-meson coupling model QCD sum rules Mean field models Coupled-channel models with contact interactions Perturbation by pion exchanges 1. Introduction to charm (bottom) nuclei D(*) (B(*)) meson in nuclear matter 1. D (B) meson and nucleon interaction 2. Modifications of D (B) meson chiral condensate, gluon condensate, ... 3. Modifications of nuclear structure glue-like role? → L. Tolos A. Yokota Y. Yamaguchi K. Suzuki Cf. Kondo effect K.Sudoh, S.Y., PRC88, 015201 (2013) 1. Introduction to charm (bottom) nuclei D(*) (B(*)) meson in nuclear matter → L. Tolos A. Yokota Y. Yamaguchi K. Suzuki 1. D (B) meson and nucleon interaction 2. Modifications of D (B) meson chiral condensate, gluon condensate, ... Cf. Kondo effect K.Sudoh, S.Y., PRC88, 015201 (2013) 3. Modifications of nuclear structure glue-like role? 4. Probe for “gluon dynamics” New from heavy quark! 2. Mass formula with 1/mQ expansion Heavy Quark Effective Theory (HQET) 2. Mass formula with 1/mQ expansion Heavy quark effective theory (HQET) 1/mQ expansion Light quarks & gluons HQET Qv 2. Mass formula with 1/mQ expansion Heavy quark effective theory (HQET) 1/mQ expansion Light quarks & gluons HQET Qv Mass of heavy meson H containing a heavy quark Q (in vacuum) rest frame 2. Mass formula with 1/mQ expansion Heavy quark effective theory (HQET) 1/mQ expansion Light quarks & gluons HQET Qv Mass of heavy meson H containing a heavy quark Q (in vacuum) rest frame Matrix elements LO scale anomaly NLO O(1/mQ) chromoelectric gluon chromomagnetic gluon Bigi, Shifman, Uraltsev, Vainshtein, PRD52, 196 (1995) Neubert, PLB322, 419 (1994) “Virial theorem” 3. Anti-D (B) meson in nuclear medium In-medium Heavy Quark Effective Theory (HQET) 3. Anti-D (B) meson in nuclear medium Heavy quark effective theory (HQET) 1/mQ expansion Light quarks & gluons HQET Qv Mass of heavy meson H containing a heavy quark Q (in medium at T and ρ) rest frame Matrix elements LO scale anomaly NLO O(1/mQ) chromoelectric gluon chromomagnetic gluon 3. Anti-D (B) meson in nuclear medium Heavy quark effective theory (HQET) 1/mQ expansion Light quarks & gluons HQET Qv Mass of heavy meson H containing a heavy quark Q (in medium at T and ρ) rest frame Matrix elements LO scale anomaly NLO O(1/mQ) chromoelectric gluon chromomagnetic gluon 3. Anti-D (B) meson in nuclear medium Heavy quark effective theory (HQET) 1/mQ expansion Light quarks & gluons HQET Qv 1/mQ Mass of heavy meson H containing a heavy quark Q (in medium at T and ρ) rest frame Matrix elements LO scale anomaly NLO O(1/mQ) chromoelectric gluon chromomagnetic gluon 3. Anti-D (B) meson in nuclear medium Λ , λ1 and λ2 change in medium. Gluon fields change in medium. gluon Q Ea, Ba 3. Anti-D (B) meson in nuclear medium Non-perturbative dynamics by light quarks and gluons?? Heavy meson effective theory (HMET) LO + NLO 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Heavy-meson effective field and separation of momentum P(*)=(Qq)spin 0 (1) vector meson pseudoscalar meson Spin degeneracy at LO four-velocity + residual momentum 1/M correction (NLO) : uncertainty of four-velocity or residual momentum (change of frame with v to frame with w) Hv(x) Hw(x) v w Luke, Manohar, PLB286, 348 (1992), Kitazawa, Kurimoto, PLB323, 65 (1994) 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Heavy-meson effective field and separation of momentum P(*)=(Qq)spin 0 (1) vector meson pseudoscalar meson Spin degeneracy at LO four-velocity + residual momentum 1/M correction (NLO) : uncertainty of four-velocity or residual momentum (change of frame with v to frame with w) Hv(x) v p/M Hw(x) w Luke, Manohar, PLB286, 348 (1992), Kitazawa, Kurimoto, PLB323, 65 (1994) 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Axial-currents composed by Hv : 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Axial-currents composed by Hv : HQSS conserved (Γ=1, iγ5, γμ) O(1/M0) or O(1/M1) HQSS=Heavy quark spin symmetry 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Axial-currents composed by Hv : HQSS broken (Γ=γμγ5, σμν) smaller than or equal to O(1/M1) HQSS=Heavy quark spin symmetry 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Axial-currents composed by Hv : HQSS broken (Γ=γμγ5, σμν) smaller than or equal to O(1/M1) HQSS=Heavy quark spin symmetry 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Axial-currents composed by Hv : HQSS conserved O(1/M0) or O(1/M1) HQSS broken O(1/M1) HQSS=Heavy quark spin symmetry 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Effective Lagrangian for HMET Kitazawa, Kurimoto, PLB323, 65 (1994) P-P* mass splitting Axial-vector current by pions H pion axial-current coupling g1, g1/M, g2/M H 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Effective Lagrangian for HMET --- How to fix couplings g, g1 and g2? --Kitazawa, Kurimoto, PLB323, 65 (1994) LO NLO NLO Lattice QCD simulations by Detmold, Lin, Meinel, PRD.85, 114508 (2012) g g=0.4-0.5 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Effective Lagrangian for HMET --- How to fix couplings g, g1 and g2? --Kitazawa, Kurimoto, PLB323, 65 (1994) LO NLO NLO Decay width of D* → Dπ (PDG2012) Constraint on g1 and g2 We assume g1=0. (Conclusion is not qualitatively changed.) ( g, g1/MD, g2/MD ) = (0.5, 0, -0.07) for g=0.5 (Set 1) (0.4, 0, -0.17) for g=0.4 (Set 2) 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D(*) (B(*)) meson in nuclear matter N N-1 N N-1 N N-1 Cf. Λ-Σ mixing in nuclear matter anti-D meson anti-D* meson 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D(*) (B(*)) meson in nuclear matter N N-1 N N-1 N N-1 Cf. Λ-Σ mixing in nuclear matter anti-D meson anti-D* meson Kitazawa, Kurimoto, PLB323, 65 (1994) 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D(*) (B(*)) meson in nuclear matter g →g + (g1-g2)/M N N-1 N N-1 1/M corrections from HMET g →g + (g1+g2)/M N N-1 g →g + (g1+g2)/M Cf. Λ-Σ mixing in nuclear matter anti-D meson anti-D* meson Kitazawa, Kurimoto, PLB323, 65 (1994) 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D(*) (B(*)) meson in nuclear matter ρ=0.17 fm-3 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D(*) (B(*)) meson in nuclear matter @ mediu m @ vacuum ρ=0.17 fm-3 scale anomaly in QCD about 0.9 suppression in gluon condensate (T. Cohen et al. 1992) chromoelectric gluon chromomagnetic gluon 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D(*) (B(*)) meson in nuclear matter @ mediu m @ vacuum ρ=0.17 fm-3 scale anomaly in QCD about 0.9 suppression in gluon condensate (T. Cohen et al. 1992) chromoelectric gluon chromomagnetic gluon 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D(*) (B(*)) meson in nuclear matter @ mediu m @ vacuum ρ=0.17 fm-3 scale anomaly in QCD about 0.9 suppression in gluon condensate (T. Cohen et al. 1992) chromoelectric gluon chromomagnetic gluon 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D(*) (B(*)) meson in nuclear matter @ mediu m @ vacuum (0.4, 0, -0.17) ( g, g1/MD, g2/MD ) = (0.5, 0, -0.07) scale anomaly in QCD Λ → suppressed Energy contribution from gluons becomes small. (Suppression of quantum effects.) normal density 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D(*) (B(*)) meson in nuclear matter @ mediu m @ vacuum (0.4, 0, -0.17) ( g, g1/MD, g2/MD ) = (0.5, 0, -0.07) scale anomaly in QCD Λ → suppressed Energy contribution from gluons becomes small. (Suppression of quantum effects.) normal density chromoelectric gluon λ1 → enhanced Kinetic energy becomes large, due to the binding energy. normal density 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D(*) (B(*)) meson in nuclear matter @ mediu m @ vacuum (0.4, 0, -0.17) ( g, g1/MD, g2/MD ) = (0.5, 0, -0.07) scale anomaly in QCD Λ → suppressed Energy contribution from gluons becomes small. (Suppression of quantum effects.) normal density chromoelectric gluon λ1 → enhanced Kinetic energy becomes large, due to the binding energy. chromomagnetic gluon λ2 → suppressed D-D* (B-B*) splitting become small. normal density 3. Anti-D (B) meson in nuclear medium Gluon dynamics in “single particle state” in atomic nuclei with anti-D(*) (Λc) 12 12 anti-D C (Λc C) thr. B.E. e.s. j+1/2 j-1/2 g.s. 3. Anti-D (B) meson in nuclear medium Gluon dynamics in “single particle state” in atomic nuclei with anti-D(*) (Λc) gluon Gluon dynamics 12C ( 12C) thr. anti-D Λc can be probed Q for each s.p.s. !? a a E ,B B.E. j+1/2 e.s. s.p.s. (n2S+1L ) of anti-D(*) (Λc) j-1/2 g.s. J → Λ, λ1, λ2(mQ) @n2S+1LJ scale anomaly, chromoelectric gluon, chromomagnetic gluon for each s.p.s. 3. Anti-D (B) meson in nuclear medium Gluon dynamics in “single particle state” in atomic nuclei with anti-D(*) (Λc) gluon Gluon dynamics 12C ( 12C) thr. anti-D Λc can be probed Q for each s.p.s. !? a a E ,B B.E. j+1/2 e.s. s.p.s. (n2S+1L ) of anti-D(*) (Λc) j-1/2 g.s. J → Λ, λ1, λ2(mQ) @n2S+1LJ scale anomaly, chromoelectric gluon, chromomagnetic gluon for each s.p.s. Heavy hadron mass spectrum Gluon dynamics 3. Anti-D (B) meson in nuclear medium Cf. Yamaguchi’s presentation Few-body calculations chromoelectric gluon chromomagnetic gluon → enhanced → suppressed Two-body S.Y., K.Sudoh, Phys. Rev. D80, 034008 (2009) Y.Yamaguchi, S.Ohkoda, S.Y., A.Hosaka, Phys. Rev. D84, 014032 (2011); ibid. 85, 054003 (2013) Three-body Y.Yamaguchi, S.Y., A.Hosaka, arXiv:1309.4324 [nucl-th] 4. Summary & perspectives We considered 1/mQ expansion up to O(1/mQ). We discussed charm (bottom) hadron mass in nuclear medium. By probing of P(*) meson mass in nuclear matter, we find ... (1) Scale anomaly from QCD is suppressed. (2) Chromoelectric gluons are enhanced. (3) Chromomagnetic gluons are suppressed. Experimental studies for charmed nuclei at J-PARC and GSI-FAIR. 4. Summary & perspectives We considered 1/mQ expansion up to O(1/mQ). We discussed charm (bottom) hadron mass in nuclear medium. By probing of P(*) meson mass in nuclear matter, we find ... (1) Scale anomaly from QCD is suppressed. (2) Chromoelectric gluons are enhanced. (3) Chromomagnetic gluons are suppressed. Experimental studies for charmed nuclei at J-PARC and GSI-FAIR. 4. Summary & perspectives We considered 1/mQ expansion up to O(1/mQ). We discussed charm (bottom) hadron mass in nuclear medium. By probing of P(*) meson mass in nuclear matter, we find ... (1) Scale anomaly from QCD is suppressed. (2) Chromoelectric gluons are enhanced. (3) Chromomagnetic gluons are suppressed. Experimental studies for charmed nuclei at J-PARC and GSI-FAIR. 4. Summary & perspectives We considered 1/mQ expansion up to O(1/mQ). We discussed charm (bottom) hadron mass in nuclear medium. By probing of P(*) meson mass in nuclear matter, we find ... (1) Scale anomaly from QCD is suppressed. (2) Chromoelectric gluons are enhanced. (3) Chromomagnetic gluons are suppressed. Experimental studies for charmed nuclei at J-PARC and GSI-FAIR. “Gluons” can be researched in charm/bottom systems !! Quarks & Gluons Chiral symmetry m→0 Quarks & Gluons Heavy Chiral quark symmetry symmetry m→0 m→∞ What is D/D-nucleon interaction ? D and nucleon D*+N (2947 MeV) D+N (2803 MeV) Only DN and D*N channel C<0 differen t D and nucleon D*+N (2947 MeV) D+N (2803 MeV) Σc(2800) 1(??) π+Σc* (2658 MeV) Λc(2625) 0(3/2-) Λc(2595) 0(1/2-) C>0 π+Σc (2593 MeV) `Exotic channel‘ cqqq SY and Sudoh, PRD80, 034008 (2009) q Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012) `Baryon channel‘ cqqq q Hosaka, arXiv:1301.4557 [hep-ph] Yamaguchi, Ohkoda, SY, What is D/D-nucleon interaction ? D and nucleon D*+N (2947 MeV) D+N (2803 MeV) Only DN and D*N channel C<0 differen t D and nucleon D*+N (2947 MeV) D+N (2803 MeV) Σc(2800) 1(??) π+Σc* (2658 MeV) Λc(2625) 0(3/2-) Λc(2595) 0(1/2-) C>0 π+Σc (2593 MeV) `Exotic channel‘ cqqq SY and Sudoh, PRD80, 034008 (2009) q Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012) `Baryon channel‘ cqqq q Hosaka, arXiv:1301.4557 [hep-ph] Yamaguchi, Ohkoda, SY,